prediction and measurement of radiated emissions based on

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Prediction And Measurement Of Radiated Emissions Based On Prediction And Measurement Of Radiated Emissions Based On

Empirical Time Domain Conducted Measurements Empirical Time Domain Conducted Measurements

Larry Freeman University of Central Florida

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PREDICTION AND MEASUREMENT OF RADIATED EMISSIONS BASED ON EMPIRICAL TIME DOMAIN CONDUCTED MEASUREMENTS

by

LARRY FREEMAN B.S.E.C.E, The Ohio State University

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science

in the School of Electrical Engineering and Computer Science in the College of Engineering and Computer Science

at the University of Central Florida, Orlando, Florida

Summer Term 2006

ABSTRACT

This thesis develops a novel method to predict radiated emissions measurements. The

techniques used are based on standard Electromagnetic Compatibility (EMC)

qualification test methods. The empirical data used to formulate the final results was

restricted to pertinent data protocol waveforms however the entire method may be

applied to any waveforms for which empirical radiated emissions have been measured.

The method provides a concise means for predicting worst case radiated emissions

profiles based on empirical measured data.

ii

ACKNOWLEDGMENTS

I would like to acknowledge Tom, Sean, Charlie, and Joe. Four wonderful supervisors; I

am a better engineer and person for having known you all. Thank you for all your

patience, humor, and inspiration. A special thanks to Prof. Thomas Wu, for all his

guidance and support in this endeavor; he is a superb professional and scholar.

iii

TABLE OF CONTENTS

LIST OF FIGURES ........................................................................................................... vi

1. Introduction................................................................................................................. 1

1.1. Premise................................................................................................................ 1

1.2. Past Research ...................................................................................................... 3

1.3. Outline................................................................................................................. 4

1.4. Objective ............................................................................................................. 5

2. Waveform Measurement ............................................................................................. 6

3. Waveform Transform .................................................................................................. 9

3.1. Technique to Convert into Matlab ...................................................................... 9

3.2. Verification........................................................................................................ 10

3.3. Matlab Transform Verification.......................................................................... 11

4. Antenna Coupling ..................................................................................................... 13

4.1. EMC Certification Setup................................................................................... 13

4.2. Coupling Model Derivation .............................................................................. 14

4.2.1. First Transmission Line Equation ............................................................. 14

4.2.2. Second Transmission Line Equation......................................................... 18

4.3. Solution of Transmission Line Equations ......................................................... 19

4.4. Measurement Parameters .................................................................................. 23

4.5. Measurement Controlled Setup......................................................................... 24

4.6. Empirical Measurements .................................................................................. 26

4.6.1. Antenna Factor Interpolation .................................................................... 27

4.7. Impedance Factor.............................................................................................. 28

iv

5. Radiated Emissions Profile Prediction...................................................................... 30

5.1. Prediction Example........................................................................................... 30

6. Conclusions............................................................................................................... 34

6.1. Overall Technique ............................................................................................. 34

6.2. Matlab Implementation..................................................................................... 34

6.2.1. Matrices Manipulation in Matlab.............................................................. 34

6.3. Empirical Measurements .................................................................................. 35

6.4. Recommendations............................................................................................. 35

APPENDIX A: MEASUREMENT ANTENNA FACTORS ............................................ 37

APPENDIX B: SAMPLE OF MEASURED WAVEFORMS........................................... 40

APPENDIX C: MEASUREMENT SETUP PICTURES.................................................. 43

APPENDIX D: IMPEDANCE FACTOR PLOTS FOR TWISTED PAIR

MEASUREMENTS.......................................................................................................... 47

LIST OF REFERENCES.................................................................................................. 53

v

vi

LIST OF FIGURES

Figure 1-1: Conducted Emission to Radiate Susceptibility Scenario ................................. 2

Figure 1-2: Process Outline ................................................................................................ 4

Figure 2-1: Time Domain Measurement Conversion Graph .............................................. 7

Figure 2-2: Time Domain Measurement with Ringing....................................................... 7

Figure 2-3: Sample Corrupted Measured Waveform.......................................................... 8

Figure 3-1: Power Density of Frequency Content .............................................................. 9

Figure 3-2: Matlab Program Functional Flowchart .......................................................... 10

Figure 3-3: Measured Waveform ...................................................................................... 12

Figure 3-4: Matlab DFT Waveform .................................................................................. 12

Figure 4-1: Generic Radiated Emissions Test Setup......................................................... 13

Figure 4-2: Two Wire Coupling Model Geometry............................................................ 14

Figure 4-3: Physical Representation of Coupling Derivation........................................... 15

Figure 4-4: Incremental Representation............................................................................ 15

Figure 4-5: DM and CM Current Action .......................................................................... 17

Figure 4.6: Circuit Representation.................................................................................... 20

Figure 4-7: Detailed Picture of Controlled Measurement Setup ...................................... 25

Figure 4-8: Scope Capture of Measurement Waveform ................................................... 26

Figure 4-9: Antenna Factor Interpolation ......................................................................... 27

Figure 4-10: Antenna Factor Divergence Error ................................................................ 28

Figure 5-1: Time Domain of TP-2T Waveform ................................................................ 30

Figure 5-2: FFT of TP-2T Waveform ............................................................................... 31

Figure 5-3: Predicted Radiated Emission Profile.............................................................. 32

Figure 5-4: Predicted Radiated Emission Profile Using Nominal Value for Impedance

Factor ........................................................................................................................ 33

Figure A-1: Rod Antenna Factor....................................................................................... 38

Figure A-2: Bi-conical Antenna Factor............................................................................. 38

Figure A-3: Double Ridge Horn Antenna Factor.............................................................. 39

Figure A-4: Horn Antenna Factor ..................................................................................... 39

Figure B-1: Sample 1 Scope Capture, FFT of Scope Capture, and RE Measurement ..... 41

Figure B-2: Sample 2 Scope Capture, FFT of Scope Capture, and RE Measurement ..... 42

Figure C-1: 10 kHz-30MHz Measurement Setup............................................................. 44

Figure C-2: 30 MHz-200MHz Measurement Setup ......................................................... 44

Figure C-3: 200MHz-1GHz Measurement Setup ............................................................. 45

Figure C-4: Waveform Generator ..................................................................................... 45

Figure C-5 Termination Shielding .................................................................................... 46

Figure C-6: Feed and Bulkhead ........................................................................................ 46

Figure D-1: Impedance Factor for TP-1T Waveform ....................................................... 48









vii

1. INTRODUCTION

The profession of Electromagnetic Interference (EMI) and Electromagnetic Compatibility

(EMC) engineering has long been governed by design practices established through

empirical measurement. Often detailed analysis isn’t an option, due to the sheer

complexity of the phenomena involved. The necessary parameters are either impossible

to obtain or require a nearly complete design to be of any real pertinence. The end result

is a design driven by what has worked in the past. This often leads to more stringent

design guidelines than are necessary. Many times a design effort has been driven by

these restrictive measures, that often have little or no basis, other than it is what has been

done before.

1.1. Premise

All electrical devices sold in the United States for commercial or military use are required

by law to undergo a battery of certification tests; to ensure their proper operation will not

have undesirable electrical effects on the environment of their intended use. For

example, the Federal Communications Commission (FCC) restricts the amount of

radiated emissions allowed in order that other electrical devices, such as television

transmitters, cell towers, etc., do not have their transmissions inadvertently hindered.

Compliance to these requirements may have dire consequences in critical areas such as

aerospace vehicle controls, medical devices, and communications.

1

Most all of these EMC standards contain a suite of various tests. The most common are

Conducted Susceptibility (CS), Conducted Emissions (CE), Radiated Emissions (RE),

and Radiated Susceptibility (RS). Most engineers over simplify these into two

categories, “Stuff that gets out are emissions. Stuff that gets in is susceptibility”.

However they are much more complex. For example in Figure 1.1, within a chassis or

box one Printed Circuit Board (PCB) may have conducted emissions from its trace that

radiate susceptibility to another PCB. From the first card’s point of view this is initially a

conducted emissions problem that manifests itself into a radiated emission that causes a

radiated susceptibility of the second PCB card.

Existing methods require the use of invasive tools. For example, current monitor probes

are frequency dependent and must be wrapped around the conductor being tested. This

may be impractical or even impossible. The only other alternative is to bring an

Engineering Design Unit (EDU) into the test chamber to perform RE testing. This is

particularly unappealing for several reasons; usually it will affect schedule and cost. Not

to mention EDU units are never meant to be fully compliant (only functional), often they

require significant modifications to meet their functional obligation.

Figure 1-1: Conducted Emission to Radiate Susceptibility Scenario

2

The objective of this thesis is to investigate an approach that seeks to bridge the gap

between empirical measurement and derived analysis.

1.2. Past Research

A thorough review for similar research efforts was performed. This literature survey

included several texts, the World Wide Web, and the IEEE EMC society archives dating

back to 1955 [1]. Many topics covered some aspect of this research effort. For example,

a myriad of papers discussing conducted emissions, radiated emissions, or the Fast

Fourier Transform were found. Even several papers relating the two were found. Works

by Professor Clayton Paul and Donald White detail theoretical aspects but do not

correspond easily to measured parameters. Few papers sought to specifically relate

measured data. Instead they chose to simply verify with measured results.

The other significant differences were the use of voltage measurements versus current

measurements. This is attributed to the fact that 99% of these papers concerned

themselves with power line measurements that had varying impedances. Current probes

present other issues, these are discussed later. The other significant discriminator was the

use of special equipment or measurement fixtures. The use of special equipment or

fixtures was deemed much too restrictive to be of use for this effort. The result of this

thesis is to provide the details by which an individual using simple techniques and

equipment commonly found around an EMC laboratory can perform preliminary

measurements and formulate a prediction of compliance to radiated emissions. This is

best done using empirical measurement data.

3

1.3. Outline

First the overall process being followed is presented; step by step. Then an elementary

EMC certification setup is discussed; this explains the rationale behind such an endeavor

and highlights the conception of specific physical modeling discussed later. Then a wire

coupling model is presented along with the justification and explanation for its

expansion. The initial measurement collection and transformation processes are detailed.

Next the entire process is demonstrated in its intended sequence. Finally, a comparison is

made between the predicted emissions profile and an actual empirically measured

emissions profile, along with an explanation or hypothesis for any deviation.

Figure 1-2: Process Outline

4

1.4. Objective

It is important to point out the overall objective of this research. The goal of this research

is not to predict the precise emissions profile but rather to envelope its worst case profile,

using relatively straightforward data measurements. This will give the EMC design

engineer an early look at what is to be expected through the use of real measurement

data. This will allow a design to have a much higher certainty of compliance to measured

emissions standards. Ideally the measurement data gathered from consecutive

measurements will be used to establish a database. Then an overall notion of accuracy

can be assessed in conjunction with strong empirical data. The end result of this work is

to formulate a process, which can be implemented continuously and enhanced each time

it is employed.

5

2. WAVEFORM MEASUREMENT

During an EMC certification test, conducted emissions are most always directly related to

radiated emission profiles. Radiated emissions from structures or a mechanical chassis

are common, but radiated emissions from cabling are far more prevalent. This is the

main reason behind the focused scrutiny on cabling of this paper. Conductor cabling

handles two distinct signals, digital and analog.

Typical for digital lines the frequency content is simply derived from transition rates [9].

Figure 2.1 shows a standard transform table used to predict the potential frequency

content using known transition rates. Analog transmissions are defined accordingly.

However neither of these techniques account for the unexpected variations that are

certain to occur. For example, ringing would not be accounted for using the transition

rate technique discussed, see Figure 2.2. From the figure it is easy to see how inadvertent

effects such as ringing can be overlooked by simply using the transition table. A better

more definitive approach would be to simply measure each transmission line.

This may be accomplished using a current clamp or voltage probe. The current clamp is

physically large and made of ferromagnetic material, it requires at least one turn for the

transformer action to occur. Current clamps are also frequency dependent. All of this

makes current clamps extremely cumbersome and intrusive. For that reason a voltage

measurement was deemed more reasonable. Since the transmission line impedance is

known it is a simple conversion to get the current value.

6

Figure 2-1: Time Domain Measurement Conversion Graph

A simple waveform measurement of the conducted waveform taken in the time domain is

easy to obtain using an oscilloscope. Certain oscilloscope measurement parameters such

as sample rate and time reference must be established in order to guarantee a uniformed

approach; these are discussed in a later section. The measured waveform can then be

transformed into the frequency domain.

-15

-10

-5

0

5

10

15

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Frequency [MHz]

Ampl

itude

[V

]

Ti me [s]

Figure 2-2: Time Domain Measurement with Ringing

7

Modern oscilloscopes have the capability to transform time domain measurements into

the frequency domain, however not all oscilloscopes use the same Fourier transform

techniques. While most all of the oscilloscope manufacturers use the Fast Fourier

Transform, many use completely different weighting functions and versions of the

mathematical technique. For the purposes of this effort it was deemed much too

restrictive to rely on one particular manufacturer’s technique or method. Therefore each

waveform measurement was exported into a standard ASCI text file format, interpolated

and then converted into Matlab for manipulation. Figure 2.3 shows a sample of a data

waveform that has been corrupted with random noise.

Figure 2-3: Sample Corrupted Measured Waveform

8

9

3. WAVEFORM TRANSFORM

The next step is to take the measured waveform data, shown in Figure 2.3 and interpolate

it into Matlab. Figure 3.1 shows how the FFT can highlight a specific frequency of

concern. The specific DFT methodology used is outlined in a later section. The end

result is an accurate profile of all the frequencies that warrant consideration when

deriving the emissions profile envelope.

Figure 3-1: Power Density of Frequency Content

3.1. Technique to Convert into Matlab

A program, implemented in the Matlab programming language is listed in appendix A.

As mentioned earlier, certain waveform parameters must be standardized, such as sample

rate, time reference, and duration. The Matlab program imports the waveform data,

translates from a standard ASCI text file and performs the DFT. The program outputs are

10

the vectors containing the DFT amplitude and frequency reference and plots of the

various waveform data. A simple functional diagram is shown in Figure 3.2.

Figure 3-2: Matlab Program Functional Flowchart

3.2. Verification

Before any further consideration a verification step was performed. Aside from the

obvious sanity check, this step allowed for the identification of any unintentional

frequency content. For example, if an unidentified frequency component is discovered it

can be investigated. The measured waveform should be taken from preliminary

engineering designs, even bench top models, to allow for adequate time to correct the

design.

Unintentional frequency content may be a result of the preliminary design and not a part

of the finished product. For example, the final design may be implemented using DC

power from a vehicle battery, this source is by definition not likely to cause conducted

transients. However the design model could be powered from a DC power supply with a

switching rectifier that produces frequency content into the measured waveform. The

verification step should consist of, as a minimum, a preliminary survey of the intended

frequency content for analog transmissions and a comparison with Figure 2.1, for known

digital transition rates.

3.3. Matlab Transform Verification

In order to verify the accuracy of the Matlab program a square wave was measured on the

oscilloscope, imported and transformed using the Matlab program in appendix A. This

same waveform was fed directly into an Agilent spectrum analyzer and measured directly

across frequency. Each measurement was then captured as an image file; both files are

shown below as Figures 3.5 and 3.6. This strong correlation demonstrates the accuracy

of the Matlab implemented transform.

11

12

Figure 3-3: Measured Waveform

Figure 3-4: Matlab DFT Waveform

4. ANTENNA COUPLING

The principal used to formulate the emissions antenna model is to determine the induced

voltage due to an incident electromagnetic wave upon a wire suspended overtop of a

ground plane. This is pertinent because almost all EMC radiated emissions certification

testing uses this setup or one similar to it. This is true for both forms of radiated

emissions testing, commercial and military. The mathematical derivation of this

technique was originally documented by Edward Vance [2] and Alberta Smith [3]. The

formulas and derivation are delineated in the following sections with greater detail and

clearer nomenclature added where deemed necessary.

4.1. EMC Certification Setup

In the interest of uniformed scrutiny almost all radiated emissions tests use the same

setup approach, mainly with the Equipment Under Test (EUT) and its supporting

conductors being suspended above a ground plane. In the interest of simplicity the

typical setup used in Mil-Std-461E is used for this paper. Figure 4.1 below shows a

diagram of this setup.

Figure 4-1: Generic Radiated Emissions Test Setup

13

4.2. Coupling Model Derivation

4.2.1. First Transmission Line Equation

The initial coupling model is derived from that of a two wire transmission line. Figure

4.2 shows the geometry of the two wire coupling model. This has a strong correlation to

the eventual setup approach, a single wire above a ground plane, especially when

considering the image plane induced by the ground plane. This correlation is expanded

upon further in the next section.

Y

X

Z

Z 1 Z 2Z0

E(x,y,z,ω)

H(x,y,z,ω )

Z=0 Z=l

Figure 4-2: Two Wire Coupling Model Geometry

Starting with Maxwell’s equation for the curl of the electric field over an incremental

surface as shown in Figures 4.3 and 4.4, and using Stokes theorem to integrate, the

induced voltage is derived as follows:

dSBdlEdSE ⋅−=⋅=⋅×∇ ∫∫∫ SCSjω)( (1)

Evaluating the line integral over the contour that bounds the surface, using , we

have

dxdzdS =

( ) ( )[ ] ( ) ( )[ ]

( ) dzdxzxBj

zdzEzbExdzxEzzxEzz

z

b

Y

zz

z ZZ

b

XX

,

,0,,,

0

0

∫ ∫∫∫

Δ+

Δ+

−=

−−−Δ+

ω (2)

14

Figure 4-3: Physical Representation of Coupling Derivation

Figure 4-4: Incremental Representation

Dividing by the incremental step and taking the limit as it approaches zero gives

( ) ( ) ( )[ ] ( ) xdzxBjzEzbEdxzxEz

b

YZZ

b

X ∫∫ −=−−∂∂

00

,,0,, ω (3)

The field terms delineated are the total scattered and incident fields. The voltage between

the two wires is defined as

15

(4) ( ) ( )∫−=b

X xdzxEzV0

,

Using this relation the first term of (3) may be re-written as

( ) ( )zVz

xdzxEz

b

X ∂∂

−=∂∂∫0 , (5)

Using the definition for incremental voltage

zRIzEZ Δ⎟⎠⎞

⎜⎝⎛=Δ

21 (6)

and substituting this relation into (3), we have

( ) ( ) ⎟⎠⎞

⎜⎝⎛ −

=−2

,0, 121

IIRzEzbE ZZ (7)

where represents the distributed resistance in resistance per length, represent

the total current within each wire. From the convention shown in Figure 4.5, the common

mode (CM) and differential mode (DM) currents are separated as

1R 21 and II

⎟⎠

⎞⎜⎝

⎛ +=⎟

⎠

⎞⎜⎝

⎛ −=

2,

21212 II

III

I CMDM (8)

Since the measured time domain data is always differential mode; this is because

common mode carries no information; it is convenient to use (7) and the first part of (1)

to restrict the second term of (2) to DM current with [6][8]

( ) ( )zIzI DM= (9)

( ) ( ) ( )zIRzEzbE ZZ =− ,0, (10)

Finally the third term of (3) can be divided into its incident and scattered components as

follows

(11) ( ) ( ) ( )dxzxBjdxzxBjdxzxBjb s

Y

b iY

b

Y ∫∫∫ +=000

,,, ωωω

16

The reason for this is that the magnetic field originating from the DM current is what

causes the scattered magnetic field component. The reasoning behind this phenomenon is

that DM fields cancel, while CM fields combine. The difference between the two

differential fields results in a scattered element.

Figure 4-5: DM and CM Current Action

Next the inductance per unit length of transmission line Δz is given by

)(1 zI

zLsyΦ

−=Δ (12)

where is the distributed inductance per unit length and 1L syΦ is the incremental surface

scattered flux from between the conductors. By rearranging (12) to

)(1 zILz

sy −=

Δ

Φ (13)

in terms of the flux

(14) ∫∫ ∫∫ Δ===ΦΔ+ b s

ys

b sy

zz

z

sy

sy dxzxBzdxdzBdsB

00),(

we have

17

∫=Δ

Φ b sy

sy dxzxBz 0

),( (15)

Therefore, (13) and (15) give

∫ (16) −=b s

y zILdxzxB0 1 )(),(

By substituting (16) into (11), we have

(17) ( ) ( ) )(,, 100zILjdxzxBjdxzxBj

b iY

b

Y ωωω −= ∫∫

Inserting (5) and (17) into (3), we get the first transmission line equation with voltage

source as

)()()(1 zVzIZ

dzzdV

s=+ (18)

where

(19) ∫=b i

ys dxzxBjzV0

),()( ω

and 11 LjZ ω= is series impedance per unit length.

4.2.2. Second Transmission Line Equation

From Maxwell’s equations, for the scattered field, we have

(20) ss j EH ωε=×∇

from which we obtain

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂

∂−

∂∂

=z

Hy

Hj

Esy

szs

x ωε1 (21)

Since the current flows in z direction, we can assume 0// =∂∂=∂∂ yx inside the

transmission line, we obtain

⎥⎥⎦

⎤

⎢⎢⎣

⎡

∂

∂−=

zH

jE

sys

x ωε1 (22)

18

Since the voltage on the transmission line can be expressed as

(23) ∫ ∫∫ −−=−=b b s

xix

b

x dxzxEdxzxEdxzxEzV0 00

),(),(),()(

inserting (22) into (23) yields

∫ ∫+−=b b s

yix dxzxH

dzd

jdxzxEzV

0 0),(1),()(

ωε (24)

Since B Hμ= , the integration in the second term of (24) becomes

μμ

)(),(1),( 100

zILdxzxBdxzxHb s

y

b sy −== ∫∫ (25)

(16) is also used to derive (25). Inserting (25) into (24), we can obtain the second

transmission line equation as

)()()(1 zIzVY

dzzdI

s=+ (26)

where

11

1 CjL

jY ωωμε== (27)

and

(28) ∫−=b i

xs dxzxEYzI01 ),()(

4.3. Solution of Transmission Line Equations

In the following, we will discuss solution procedure for transmission line equations (18)

and (26). The circuit representation for these two equations are shown in Figure 4.6.

19

Figure 4.6: Circuit Representation

We are going to discuss the solution with current source only at first and then

discuss the solution with voltage source . And the total solution is the superposition

of these two cases.

)(zI s

)(zVs

When there is only current source, we have

⎪⎩

⎪⎨

⎧

=+

=+

)()()(

0)()(

1

1

zIzVYdz

zdI

zIZdz

zdV

s

(29)

The solution of current in (29) can be obtained using Green’s function as

(30) ( ) ( ) ( )∫∫ +=L

z

IIGs

z IGs dzzzIzIdzzzIzIzI '',)'('',)'(

0

where the Green’s functions are given by

zkjzkjIG e

ZAe

ZAI −Γ

+−=0

11

0

1 (31)

( )LzkjjkL

zkjIIG e

ZeAe

ZAI −

−− Γ

−=0

22

0

2 (32)

20

where

( )[ ]

( )Lkj

Lzkjzkj

eeeZA 2

21

'22

'0

1 121

−

−−

ΓΓ−Γ+

= (33)

[ ]( )Lkj

zkjzkj

eeeZA 221

'21

'0

2 121

−

−

ΓΓ−+Γ

= (34)

Since we are interested in the solution at Lz = , from (30) we have

(35) ( ) ( )∫=L II

Gs dzzzIzILI0

'',)'(

Assuming the transmission line is matched at both ends, which means

021 =Γ=Γ (35)

Equation (34) for derived current reduces to

2

'0

2

zkjeZA = (36)

Therefore (35) becomes

∫ −=L Lzjk

s dzezILI0

)'( ')'(21)( (37)

In order to derive an empirical solution for experimental results, we assume the

transmission line is short so that )()'( LIzI ss = is a constant, then (37) becomes

jk

eLIZ

LVLIjkL

s 21)()()(

0

−+== (38)

Likewise, when there is only current source, we have

21

⎪⎩

⎪⎨

⎧

=+

=+

0)()(

)()()(

1

1

zVYdz

zdI

zVzIZdz

zdVs

(39)

The solution for of this case should be dual to solution for of (29). Therefore,

we have

)(LV )(LI

jk

eLVLVjkL

s 21)()(

−+= (40)

Then, the solution of

⎪⎩

⎪⎨

⎧

=+

=+

)()()(

)()()(

1

1

zIzVYdz

zdI

zVzIZdz

zdV

s

s (41)

is superposition of (38) and (40), which results in

jk

eZ

LVLIZ

LV jkLs

s 21])()([)(

00

−++= (42)

From (19) and (28), we know that and both come from the incident fields. This

means that they are correlated. We can generally assume

sV sI

(43) iy

ix HZE 0)(ωα=

For uniform plane wave normal incidence 1)( =ωα , otherwise, it’s just a general

constant. From (19) and (28), we have

0

)(Z

VI s

sωα

= (44)

which means (42) can be expressed in a format as

∫=++

=− b i

xs

jkL

dxLxEYLIjke

ZLV

00

),()()()(21)(1)( ω

ωαωα (45)

22

where

)(21)(1

)(21)(1)(

01 ωα

ωαωωα

ωαω ++−=

++−=

−−

ZeCj

jkeY

jkLjkL

(46)

4.4. Measurement Parameters

By the reciprocal property of antennas the incident electric field may be interpolated to a

distance of one meter; the standardized measurement distance. The driving current

source is the measured oscilloscope waveform, initially interpolated into the frequency

domain, using the technique outlined. From (45), because we are interested in E-field

radiation, we begin by taking the absolute value of each component.

( ) ( ) ( )dxzxEZ

LVZb

ix ,

00∫=⎟⎟

⎠

⎞⎜⎜⎝

⎛ω (47)

Note that (47) has only a vertical component of the E-field. This is consistent with the

measurement setup and the definition for the E-field component. By definition the

measured radiated emission is a measurement of the E-field component, it has no phase

component and correlates to the absolute value of the E-field component.

However, the time domain measurement is a voltage measurement. This was deemed the

most unobtrusive since it is relatively simple and requires no correction other than to

divide by the characteristic impedance of the transmission line. Equation (47) divides the

current source by the characteristic impedance and solves for the impedance factor in

terms of the time domain voltage waveform.

23

( )( )

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

∫

0

0

)(

,

ZLV

dxzxEZ

bix

ω (48)

However, the E-field component in (47) does not directly correlate to the radiated

measurement. This is because the radiated emissions measurement uses antenna factors

that account for the antenna loss. These factors are simply programmed into the receiver

system and added to the detected E-field signal. These factors and their impact on the

measurement data are discussed in more detail in a following section.

The final step is to establish a measurable sample test setup. The challenge is to assure

direct correlation between the measurable controlled setup and that of the standard EMC

qualification setup. For the purposes of this work, the Mil-Std-461 military test setup is

used. However the controlled setup is just as applicable to virtually any standard radiated

emissions qualification test setup, commercial or military.

4.5. Measurement Controlled Setup

This setup is a simple representation of a standard Electromagnetic Compatibility

qualification test. Its main function is to provide an empirically measurable cable

antenna, so that the radiated emissions profile may be measured and then directly

correlated in terms of the parameters outlined above. This measurement data can then be

interpolated in terms of the derived mathematical form. Finally, resultant profiles based

in terms of the initial waveform capture, in the time domain, can be used to furnish a

useful prediction of the radiated emissions profile, based mainly on measured waveforms

easily captured in the time domain.

24

Penetration Plate

2 m

Load Termination5 cm Standoff

Signal Generator

Ground Plane

Measurement Antenna

Figure 4-7: Detailed Picture of Controlled Measurement Setup

Measurements across the frequency range were made using the Figure 4-7 setup. The

cabling stimulus used for this evaluation is a standard square wave pulse with the

characteristics shown in Figure 4-8.

25

Figure 4-8: Scope Capture of Measurement Waveform

4.6. Empirical Measurements

Laboratory measurements always have an unavoidable degree of uncertainty. The typical

radiated emissions equation is shown in (49) below. Note (49) has units in decibels.

LossAFEE AntennaMeasured ++= (49)

The two field components are divided into the measured electric field and the incident

electric field on the measurement antenna. The additional term is the pre-calibrated

antenna factor of the measurement antennas; these are given in appendix B. The final loss

term is due to various measurement attenuations, i.e. Component Insertion Loss, Cable

loss, etc.

26

4.6.1. Antenna Factor Interpolation

The measurement antenna factors require linear interpolation between any two

measurement points. For example, the antenna factors measurement file may not have

the exact number of measurement points that the time domain waveform will. Nor are

the files likely to have the required corresponding frequency point. Therefore a program

that first determines the closest measurement points and then linear interpolates between

them, in order to calculate a corresponding frequency component.

This interpolation technique has been implemented using a Matlab program, given in

appendix C. This technique inherently introduces a margin of error, but this margin is

low, approximately 0.01%. Once the antenna factor has been determined, it can be

subtracted from the measured field along with the loss and then the measured electric

field can be interpolated to the electric field incident on the cabling.

Figure 4-9: Antenna Factor Interpolation

27

Figure 4-10: Antenna Factor Divergence Error

4.7. Impedance Factor

From equation 37 the impedance factor has been empirically measured for a distinct

setup scenario, a twisted pair wire over a ground plane. Both conductors are 22 AWG;

this is the most commonly used conductor size for known protocols such as Mil-Std-

1553, RS-422, RS-485, and Low Voltage Differential Signal (LVDS) signal interfaces.

Distinct waveform measurements with varying rise time, fall time, and pulse width were

measured for both setups. These are listed below.

28

Setup Rise/Fall Time Pulse Width Designator

Ambient NA NA AMB

Twisted Pair 10ns 400ns TP-1

Twisted Pair 10ns 1us TP-2






Twisted Pair 1us 10us TP-8

Twisted Pair 1us 100us TP-9

The impedance factor for each measurement is shown in appendix D.

29

5. RADIATED EMISSIONS PROFILE PREDICTION

Once the incident electric field has been measured and the attenuation loss factors have

been accounted for, the radiated emissions profile can be predicted. The emissions

profile prediction uses equations (48) and (49), defined in terms of the measurement

parameters [5] [6]. The final equation is shown as equation (50) below

EmissionRadiatedEAFZV

Z =+⎟⎟⎠

⎞⎜⎜⎝

⎛× edinterpolat

0

0 (50)

5.1. Prediction Example

For simplicity we will use discrete measurement setup waveform TP-2T. Beginning with

a scope measurement shown in Figure 5.1 for waveform TP-2T the FFT was taken.

Figure 5-1: Time Domain of TP-2T Waveform

30

Figure 5-2: FFT of TP-2T Waveform

Next the amplitude in voltage was divided by 50 ohms to get the current value; this was

the size of the termination impedance used. The impedance factor was calculated

already, this is displayed in Figure D-2. From this figure the impedance factor from low

to high frequency ranges in amplitude from 10-1.5 to 102. However this impedance factor

cannot be assumed, since the objective is to predict the radiated emissions profile.

Therefore a justifiable alternative would be to use the next highest impedance factor; this

is the TP-1T impedance factor waveform. Therefore using the TP-1T impedance factor

waveform and the calculated FFT from the TP-2T time base measurement we are able to

predict the emissions profile. Figure 5-3 shows the predicted versus measured radiated

emissions profile.

31

Figure 5-3: Predicted Radiated Emission Profile

Notice the predicted emission envelope differs from the measured profile by 2dB. This

emission profile tells the cognizant design engineer precisely how much shield

attenuation this cable will require, relative to the specification limit.

Another alternative would be to simply choose a threshold impedance factor value.

Figure 5-4 shows a predicted emissions profile based on a nominal impedance factor

value of 10. Notice the peak emission is still well within the expectable margin.

32

Figure 5-4: Predicted Radiated Emission Profile Using Nominal Value for

Impedance Factor

33

6. CONCLUSIONS

6.1. Overall Technique

The overall technique is sound and intuitive. However the actual implementation was

fraught with logistics type issues. Empirical data measurements were required and this

corresponds directly to budgetary constraint on man hours, equipment time, and lab use.

This thesis is the non-recurring engineering portion of the process. From here on data

will be taken in conjunction with routine testing efforts; however this effort laid the

ground work.

6.2. Matlab Implementation

Matlab cannot support data manipulation of matrices larger than 225. This is a

fundamental design concept and cannot be overcome. The FFT requires more data

samples for better accuracy so this was a natural inhibitor. However 220 was deemed

sufficient, any more would have diminishing returns.

6.2.1. Matrices Manipulation in Matlab

Matrices require distinct mathematical techniques. For example, indexes must

correspond. This is impossible with empirical data. Receivers and Oscilloscopes have

predefined interval measurements based on environment, span, etc. Therefore

interpolation was required for all of the empirical data; this was unforeseen and led to a

lengthy delay.

34

6.3. Empirical Measurements

Empirical measurements by definition have many inherent aspects that are otherwise over

looked or just understood. However every aspect must be accounted for in a theoretical

derivation. For example, antenna correction factors are measured quantities. Antennas

are required to undergo a routine annual calibration. However the calibration is not

recorded as continuous, instead it is made at discrete points along the frequency

spectrum.

Another, severely limiting factor was the inability to view real-time data collection of the

oscilloscope measurements. Because the scope waveforms were so tightly sampled;

simple programs such as Microsoft Excel were unable to view them. Microsoft Excel is

limited to 65,536 values. This was a real problem later because some data had become

corrupted or was not recorded correctly and needed to rerecord. However the opportunity

to use laboratory time and equipment had passed.

6.4. Recommendations

The author’s goal was to establish a process, the non-recurring portion at least, so that

progressively more and more recorded measurements could be used in conjunction with

these techniques to further bolster the accuracy of this approach. The only

recommendation for improvement would be delineate according to rise time and pulse

width as much as possible. This would allow more direct comparison, even though as

this paper demonstrated it is not necessary. Also, the author would like to see the overall

technique re-programmed into an alternate program language and made into an

executable file for distribution. As it stands now each program component is not well

35

meshed with its predecessor. However, much more fluent programming is well beyond

the scope of this effort and the author’s skill.

36

APPENDIX A: MEASUREMENT ANTENNA FACTORS

37

-10.00

-5.00

0.00

5.00

10.00

0.01 0.10 1.00 10.00 100.00

Frequency In MHz

Cor

rect

ion

Fact

or In

dB

Figure A-1: Rod Antenna Factor

0.00

5.00

10.00

15.00

20.00

25.00

30.00

10.00 100.00 1000.00

Frequency In MHz

Cor

rect

ion

Fact

or In

dB

Figure A-2: Bi-conical Antenna Factor

38

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

100.00 1000.00 10000.00

Frequency In MHz

Cor

rect

ion

Fact

or I

n dB

Figure A-3: Double Ridge Horn Antenna Factor

20.00

25.00

30.00

35.00

40.00

45.00

50.00

1.00 10.00 100.00

Frequency In GHz

Cor

rect

ion

Fact

or I

n dB

Figure A-4: Horn Antenna Factor

39

APPENDIX B: SAMPLE OF MEASURED WAVEFORMS

40

Figure B-1: Sample 1 Scope Capture, FFT of Scope Capture, and RE Measurement

41

Figure B-2: Sample 2 Scope Capture, FFT of Scope Capture, and RE Measurement

42

APPENDIX C: MEASUREMENT SETUP PICTURES

43

Figure C-1: 10 kHz-30MHz Measurement Setup

Figure C-2: 30 MHz-200MHz Measurement Setup

44

Figure C-3: 200MHz-1GHz Measurement Setup

Figure C-4: Waveform Generator

45

Figure C-5 Termination Shielding

Figure C-6: Feed and Bulkhead

46

APPENDIX D: IMPEDANCE FACTOR PLOTS FOR TWISTED PAIR

MEASUREMENTS

47

Figure D-1: Impedance Factor for TP-1T Waveform


48



49



50



51


52

LIST OF REFERENCES

1. IEEE EMC Society Symposia Records 1955 to 1995, Volume IEEE001 through

IEEE004, (IEEE Publishing, New Jersey, 1995)

2. Military Handbook-241B, Design Guide for Electromagnetic Interference (EMI)

Reduction in Power Supplies, (30 September 1983)

3. E. Oran Brigham, The Fast Fourier Transform, (Prentice Hall Inc., 1974)

4. Robert A. White, Spectrum & Network Measurements, (Noble Publishing Inc.,

1993)

5. Mathworks Technical Note 1702, Using FFT to Obtain Simple Spectral Analysis

Plots, (The Mathworks Inc., 1994)

6. Albert A. Smith, Jr., Coupling of Electromagnetic Fields to Transmission Lines,

2nd Edition (Interference Control Technologies Inc., New York, 1989)

7. Edward Vance, Coupling to Shielded Cables, (John Wiley & Sons Inc., 1978)

8. Clayton R. Paul, Introduction to Electromagnetic Compatibility, (John Wiley &

Sons Inc., 1992)

9. William E. Boyce and Richard C. DiPrima, Elementary Differential Equation and

Boundary Value Problems, (John Wiley & Sons Inc., 1992)

10. Joseph J. Carr, Practical Radio Frequency Test & Measurement: A Technician’s

Handbook, (Newnes, 1999)

11. David Pozar, Microwave Engineering, (John Wiley & Sons Inc., 1998)

53

prediction and measurement of radiated emissions based on

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